Elastoplastic analysis by active macro-zones with linear kinematic hardening and von Mises materials

In this paper a strategy to perform elastoplastic analysis with linear kinematic hardening for von Mises materials under plane strain conditions is shown. The proposed approach works with the Symmetric Galerkin Boundary Element Method applied to multidomain problems using a mixed variables approach, to obtain a more stringent solution. The elastoplastic analysis is carried out as the response to the loads and the plastic strains, the latter evaluated through the self-equilibrium stress matrix. This matrix is used both, in the predictor phase, for trial stress evaluation and, in the corrector phase, for solving a nonlinear global system which provides the elastoplastic solution of the active macro-zones, i.e. those zones collecting bem-elements where the plastic consistency condition has been violated. The simultaneous use of active macro-zones gives rise to a nonlocal approach which is characterized by a large decrease in the plastic iteration number, although the proposed strategy requires the inversion and updating of Jacobian operators generally of big dimensions. A strategy developed in order to reduce the computational efforts due to the use of this matrix, in a recursive process, is shown.